3.4 Rational numbers

The rational numbers, denoted Q, take care of the problem of the integers not being closed under division by nonzero values. rational number number$rational Q`bold

3.4.1 Fractions

Let’s start by talking about fractions, also known as the rational numbers, in the way a teacher may have introduced them to you. We then relate this review to what we have in the big picture with Q.

Given a loaf of bread, if we cut it right down the middle, we say we have divided it into halves. Fraction-wise, one-half = 1/2. The two halves equal one whole loaf, so 1/2 + 1/2 = 2 × 1/2 = 1. Two halves are 2/2, which is 1. Four halves would make two loaves: 4/2 = 2.

Considering whole loaves, 1/1 is one loaf, 2/1 is two loaves, and 147/1 is one hundred and forty-seven loaves. We can represent any integer n as a fraction n/1.

To multiply fractions, we multiply the tops (numerators) together, put those over the product...